Geometry & Topology

Geodesic flow for $\mathrm{CAT}(0)$–groups

Arthur Bartels and Wolfgang Lück

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We associate to a CAT(0)–space a flow space that can be used as the replacement for the geodesic flow on the sphere tangent bundle of a Riemannian manifold. We use this flow space to prove that CAT(0)–group are transfer reducible over the family of virtually cyclic groups. This result is an important ingredient in our proof of the Farrell–Jones Conjecture for these groups.

Article information

Geom. Topol., Volume 16, Number 3 (2012), 1345-1391.

Received: 16 September 2010
Revised: 12 March 2012
Accepted: 2 June 2012
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F67: Hyperbolic groups and nonpositively curved groups

geodesic flow space $\mathrm{CAT}(0)$–groups Farrell–Jones Conjecture


Bartels, Arthur; Lück, Wolfgang. Geodesic flow for $\mathrm{CAT}(0)$–groups. Geom. Topol. 16 (2012), no. 3, 1345--1391. doi:10.2140/gt.2012.16.1345.

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